The derivation of relationships between the rainfall over a catchment area and the resulting flow in a river is a fundamental problem for the hydrologist. Inmost countries, there are usually plenty of rainfall records, but the more elaborate and expensive streamflow measurements, which are needed for the assessment of water resources or of damaging flood peaks, are often limited and are rarely available for a specific site under investigation. Modelling the way in which rainfall becomes river discharge has stimulated the imagination and ingenuity of hydrologists for over a century, but has been an important area of research in the last 40 years as digital computers have become more widely available. Catchment models are now routinely used in flood forecasting, the design of flood defences and urban drainage systems, water resources assessment, and predicting the response of ungauged catchments. The use of models in hydrology is widespread in the applications illustrated in the remaining chapters of this book.